knitr::opts_chunk$set(warning = FALSE, message = FALSE)
library(RNifti)
library(ggplot2)
library(patchwork)
library(DiagrammeR)

Permutation scheme

For the test, I have 10 subjects with complete data. This is the exchangeability structure used:

graph <- readr::read_lines('ptree.dot')
graph <- c(graph[1], 'graph [layout = circo]', graph[2:length(graph)])
DiagrammeR::grViz(graph)

Each participant has 2 runs with 7 conditions in each run. The contrast of interest subtracts the average of 3 conditions from the average of the other 4 conditions.

I first created 100 permuted design matrices based on the scheme above, shuffling rows within-participant. I then ran PALM (see config below) using each of these permuted design matrices (using -n 1000 permutations).

Design Files

Contrast

Download l3_contrast.con

/ContrastName1  Go-CR 
/NumWaves   7
/NumContrasts   1
/PPheights      1.000571e+00
/RequiredEffect     0.632

/Matrix
2.500000e-01 2.500000e-01 2.500000e-01 2.500000e-01 -3.330000e-01 -3.330000e-01 -3.330000e-01

Original Design Matrix

Download l3_contrast.mat

/NumWaves   7
/NumPoints  140
/PPheights      1.000000e+00    1.000000e+00    1.000000e+00    1.000000e+00    1.000000e+00    1.000000e+00    1.000000e+00

/Matrix
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0.000000e+00    0.000000e+00    0.000000e+00    0.000000e+00    0.000000e+00    0.000000e+00    1.000000e+00

Palm Config

Download ten_perfect_l3_con_perm_01_palmconfig.txt

# Configuration file for PALM.
# Version alpha118
, running in MATLAB 9.10.0.1602886 (R2021a).
# 27-Aug-2021 11:34:10

-i ../Go-CR.4d.dtseries.nii
-transposedata
-eb ../eb.csv
-d l3_contrast_perm_01.mat
-t ../l3_contrast.con
-n 1000
-within
-ee
-save1-p
-o ten_perfect_l3_con_perm_01
-savemetrics
-savemax

EBs

Download eb.csv

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10

Uncorrected p-values

Import data from nii

First, I look at the uncorrected p-values fro the output files perms/ten_perfect_l3_con_perm_*_dat_tstat_uncp.dscalar.nii.

fns <- sprintf('perms/ten_perfect_l3_con_perm_%02d_dat_tstat_uncp.dscalar.nii', 1:100, 1:100)
d <- data.table::rbindlist(mapply(function(x, i){
  if(file.exists(x)){
    data.table::data.table(p = as.numeric(RNifti::readNifti(x)),
      #p = 10^(-as.numeric(RNifti::readNifti(x))),
                           id = i)
  } else {
    data.table::data.table()
  }
}, fns, 1:length(fns), SIMPLIFY = FALSE))
sprintf('Range of data values (1-p): [%0.3f, %0.3f]', range(d$p)[1], range(d$p)[2])
## [1] "Range of data values (1-p): [0.000, 0.999]"
sprintf('Number of analyses of unique permuted design mats: %d', length(unique(d$id)))
## [1] "Number of analyses of unique permuted design mats: 100"

Plot distributions

Density plots for each of the 100 runs, and histograms for the data overall, and zoomed in to the left and right tails.

ggplot(d, aes(x = p)) + 
  # geom_histogram(binwidth = .05) + 
  geom_density() + 
  facet_wrap(~ id, nrow = 10) + 
  theme(strip.background = element_blank(),
        strip.text.x = element_blank(),
        axis.text = element_blank(),
        axis.ticks = element_blank()) + 
  ggplot(d, aes(x = p)) + 
  geom_histogram(binwidth = .02) + 
  ggplot(d[p>.9], aes(x = p)) + 
  geom_histogram(binwidth = .005) + 
  labs(title = 'p-1 > .90') + 
  ggplot(d[p<.1], aes(x = p)) + 
  geom_histogram(binwidth = .005) + 
  labs(title = 'p-1 < .10') + 
  plot_layout(design = "
  AAB
  AAC
  AAD")

Compute long-run error rate for uncorrected p

#these are 1-tailed tests, 1-p
ggplot(rbind(d[, .(id = 0, 
                   prop_sig = sum(p>.95)/.N,
                   run = 'Overall')],
             d[, .(prop_sig = sum(p>.95)/.N,
                   run = 'Individual'), by = 'id']), 
       aes(x = id, y = prop_sig, fill = run)) + 
  geom_col() + 
  theme(axis.text.x = element_blank()) + 
  labs(title = 'Error rate for 1-tailed test', x = '', y = 'Proportion voxels p < .05')

ggplot(rbind(d[, .(id = 0, 
                   prop_sig = sum(p<.05)/.N,
                   run = 'Overall')],
             d[, .(prop_sig = sum(p<.05)/.N,
                   run = 'Individual'), by = 'id']), 
       aes(x = id, y = prop_sig, fill = run)) + 
  geom_col() + 
  theme(axis.text.x = element_blank()) + 
  labs(title = 'Error rate for other side of 1-tailed test\n(Just in case)', x = '', y = 'Proportion voxels p < .05')

FWE p-values

Now looking at the FWE-corrected output.

fns <- sprintf('perms/ten_perfect_l3_con_perm_%02d_dat_tstat_fwep.dscalar.nii', 1:100, 1:100)
dfwe <- data.table::rbindlist(mapply(function(x, i){
  if(file.exists(x)){
    data.table::data.table(p = as.numeric(RNifti::readNifti(x)),
      #p = 10^(-as.numeric(RNifti::readNifti(x))),
                           id = i)
  } else {
    data.table::data.table()
  }
}, fns, 1:length(fns), SIMPLIFY = FALSE))
sprintf('Range of data values (1-p): [%0.3f, %0.3f]', range(dfwe$p)[1], range(dfwe$p)[2])
## [1] "Range of data values (1-p): [0.000, 0.963]"

Number of runs with at least one significant voxel: 1

Proportion of runs with at least one significant voxel: 0.01